Where: mr = Relative Magnetic Permeability (dimensionless) m = Any Given Magnetic Permeability (H/m) mo = Magnetic Permeability in Air 1.257x10-6 H/m)

Magnetic permeability is the ease with which a material can be magnetized. It is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 4p x10^-7 henry per meter or 1.257 x 10^-6 H/m in free space (a vacuum). In other materials permeability can be much different, often substantially greater than the free-space value, which is symbolized µo.

In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µ_o represents the permeability of free space and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µ_r, is given by the equation above. Relative permeability is dimensionless since it is the ratio of two permeability values expressed in the same units.

Example:

1) What is the relative permeability of a material with an absolute permeability of 5.63x10^-5H/m?

Simple plug the materials permeability and the free space permeability values in the equation and solve.

2) What is the absolute permeability of a materials with a relative permeability of 1.05

Given the equation and the permeability of free space (u₀) of 1.257x10^-6 H/mm
Rearranging this equation to solve for absolute permeability results in:

Plugging the given values into the equation produces an absolute permeability value.